As mentioned in the introduction, it is remarkable that the sampling result in [1]} which we have illuminated in Section  (Proposition REF ) is only stated and proven in \(\mathcal {F}_{\theta } L^4([-B,B])\) , for \(B > 0\)  and \(\theta \in \mathbb {R}\) . This immediately raises the question whether a similar result continues to hold if we replace \(\mathcal {F}_{\theta } L^4([-B,B])\)  by the more general spaces
\(\mathcal {F}_{\theta } L^p([-B,B]) := \left\lbrace   f : \mathbb {R}\rightarrow \mathbb {C} \,|\,  \operatorname{\exists }F \in L^p([-B,B]) : f = \mathcal {F}_\theta F_0  \right\rbrace ,\) 
